Knowledge representation systems aiming at full natural language understanding need to cover a wide range of semantic phenomena including lexical ambiguities, coreference, modalities, counterfactuals, and generic sentences. In order to achieve this goal, we argue for a multidimensional view on the representation of natural language semantics. The proposed approach, which has been successfully applied to various NLP tasks including text retrieval and question answering, tries to keep the balance between expressiveness and manageability by introducing separate semantic layers for capturing dimensions such as facticity, degree of generalization, and determination of reference. Layer specifications are also used to express the distinction between categorical and situational knowledge and the encapsulation of knowledge needed e.g. for a proper modeling of propositional attitudes. The paper describes the role of these classificational means for natural language understanding, knowledge representation, and reasoning, and exemplifies their use in NLP applications.